I am not sure that a solar recharger would be much better than dead weight in The Green Tunnel that is the AT. You could try it, obviously, but I would rate your chances of sending it home in the first 500 miles as very, very high.

As for baking on the trail, I would consider just how psychologically important it would be to you to preserve that option. Psychology is a big factor in thru-hikes (many thru-hikers would say that it is much more than half the battle), and food is a big factor in hiker psychology, but making big miles eats up (no pun) so much time and energy that you'll find that occasions for campsite baking while you're on the trail will be rare treats, widely spaced.

You should be able to satisfy the urge for baked goods when you venture off-trail for rest and resupply.